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Quintic surfaces of \(\mathbb{P}^ 3\) having a non-singular model with \(q=p_ g=0\), \(P_ 2\neq 0\). (English) Zbl 0830.14013

Summary: In this paper we construct new examples of quintic surfaces of \(\mathbb{P}^3\) having only isolated singularities \((r\) tacnodes or \(s\) double points with infinitely near a tacnode, \(r + s = 4)\) whose nonsingular model has irregularity \(q = 0\) and invariants \(p_g = 0\), \(P_2 \neq 0\). In particular, an example is found of a quintic with a non singular model of general type.

MSC:

14J17 Singularities of surfaces or higher-dimensional varieties
14N05 Projective techniques in algebraic geometry
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References:

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